When Paapa Essiedu – a much admired Romeo at the Tobacco Factory in Bristol last year – plays Hamlet for the RSC next month he will join a very small group of black and Asian actors who have been cast in the role on a British stage. When Don Warrington plays Lear in Talawa’s revival at Manchester’s Royal Exchange in April, he will be only the ninth black actor since 1930 to play the role on stage or screen in the UK.

There are two ways of looking at this. One is that we have come a long way since Donald Sinden blacked up to play Othello for the RSC in 1979, and it marks a big step forward in colour-blind casting and should be celebrated. The other is that it shows how little real change there has been in achieving a depth and breadth of diversity on our stages, and why organisations such as Act for Change have a major role to play in strengthening diversity across the arts.

Trevor Nunn’s defence of his all-white casting of The Wars of the Roses last year, and the need to counter some of the ridiculous comments over the casting of one of our finest actors, Noma Dumezweni, as Hermione in Harry Potter and the Cursed Child, reminds that there are still daily battles to be fought and won.

The British black and Asian (BBA) Shakespeare database, researched by Jami Rogers at Warwick University, has charted more than 1,200 Shakespeare productions between 1930 and 2015 and looked at the casting of black and Asian actors in those revivals. It makes for very interesting reading, not least because it points up the uncomfortable fact that while there is a significant amount of colour-blind casting in Shakespeare, black and Asian actors seldom get a chance to take the significant roles. It was a point made by east Asian actors in 2012 when the RSC staged The Orphan of Zhao with a very small number of east Asian actors involved, all of them in supporting roles. The BBA Shakespeare research demonstrates that there has been an increase in ethnic minority casting over the last 85 years, but suggests that casting directors and directors are paying lip service to colour-blind casting and often only employ black or Asian actors to play smaller roles or servants. In the case of more substantial roles, some particularly appear to be earmarked for minority casting: the nurse in Romeo and Juliet being an obvious one, played 22 times by black, Asian and minority ethnic (BAME) actors.

This suggests that although there may be opportunities for BAME actors, there is seldom an opportunity for the kind of career progression that actors need to develop their skills. Essiedu is the exception rather than the rule, and the statistics suggest that however successful he is at Hamlet, he may find it hard to extend his range into other great Shakespearean roles, particularly in the history plays. There has been little progress since David Oyelowo was the first black actor to be cast as an English monarch in Henry VI at the RSC in 2000. If you are a woman, you may get to play a witch in Macbeth but you are far less likely to get a crack at Lady M.

Don Warrington is to play King Lear at the Royal Exchange in April. Photograph: Linda Nylind for the Guardian

This does change when Shakespeare comes with a concept such as Gregory Doran’s African-set Julius Caesar in 2012. The RSC’s upcoming Hamlet is described by the director Simon Godwin as being set in a “Denmark reconceived as a modern state influenced by the ritual, beauty and cosmology of West Africa”. It raises the question: do those who run our theatres believe that a production requires relocation to justify the majority casting of black actors? Or is it only in such productions when there is a change of setting that black actors are likely to get opportunities to take major roles? If they can play the roles when the play is given a non-British setting, why can’t they be cast in the same roles in revivals that do not involve relocations?

In fact the BBA Shakespeare database further suggests that while there have been many gains in casting since 1930, the number of black and Asian actors being cast in Shakespeare revivals is not on an ever-increasing upward incline. The peak year was 2012 (the year of the Cultural Olympiad) when 182 roles were cast with BAME actors. But it has been dropping since. In 2014 only 163 roles were played by black or Asian actors.

•There is a free public event at the Tricycle theatre in north London on Friday afternoon entitled In Robeson’s Footsteps, which explores the state of British black and Asian Shakespeare today.